Álgebra lineal Ejemplos

$[\begin{array}{c} 0 & 1 & 4 \\ 0 & 1 & \frac{6}{7} \end{array}]$

Paso 1

Obtén la forma escalonada reducida por filas.

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Paso 1.1

Perform the row operation $R_{2} = R_{2} - R_{1}$ to make the entry at $2, 2$ a $0$ .

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Paso 1.1.1

Perform the row operation $R_{2} = R_{2} - R_{1}$ to make the entry at $2, 2$ a $0$ .

$[\begin{array}{c} 0 & 1 & 4 \\ 0 - 0 & 1 - 1 & \frac{6}{7} - 4 \end{array}]$

Paso 1.1.2

Simplifica $R_{2}$ .

$[\begin{array}{c} 0 & 1 & 4 \\ 0 & 0 & - \frac{22}{7} \end{array}]$

Paso 1.2

Multiply each element of $R_{2}$ by $- \frac{7}{22}$ to make the entry at $2, 3$ a $1$ .

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Paso 1.2.1

Multiply each element of $R_{2}$ by $- \frac{7}{22}$ to make the entry at $2, 3$ a $1$ .

$[\begin{array}{c} 0 & 1 & 4 \\ - \frac{7}{22} \cdot 0 & - \frac{7}{22} \cdot 0 & - \frac{7}{22} (- \frac{22}{7}) \end{array}]$

Paso 1.2.2

Simplifica $R_{2}$ .

$[\begin{array}{c} 0 & 1 & 4 \\ 0 & 0 & 1 \end{array}]$

Paso 1.3

Perform the row operation $R_{1} = R_{1} - 4 R_{2}$ to make the entry at $1, 3$ a $0$ .

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Paso 1.3.1

Perform the row operation $R_{1} = R_{1} - 4 R_{2}$ to make the entry at $1, 3$ a $0$ .

$[\begin{array}{c} 0 - 4 \cdot 0 & 1 - 4 \cdot 0 & 4 - 4 \cdot 1 \\ 0 & 0 & 1 \end{array}]$

Paso 1.3.2

Simplifica $R_{1}$ .

$[\begin{array}{c} 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$

Paso 2

The pivot positions are the locations with the leading $1$ in each row. The pivot columns are the columns that have a pivot position.

Pivot Positions: $a_{12}$ and $a_{23}$

Pivot Columns: $2$ and $3$